A210911 - OEIS

%I #23 Dec 05 2016 10:37:45

%S 1,1,4,26,168,1416,13897,153126,1893180,25796852,383636151,6177688914,

%T 106969864696,1980478817526,39015578535585,814416108606566,

%U 17947777613632128,416233580676722424,10129555365300697267,258028441032419619786,6864011282184757297896

%N Number of transitive reflexive early confluent binary relations R on n labeled elements where |{y : xRy}| <= 3 for all x.

%C R is early confluent iff (xRy and xRz) implies (yRz or zRy) for all x, y, z.

%D A. P. Heinz (1990). Analyse der Grenzen und Möglichkeiten schneller Tableauoptimierung. PhD Thesis, Albert-Ludwigs-Universität Freiburg, Freiburg i. Br., Germany.

%H Alois P. Heinz, <a href="/A210911/b210911.txt">Table of n, a(n) for n = 0..448</a>

%F E.g.f.: exp(x*exp(x*exp(x)+x^2/2)+x^2/2*exp(x)+x^3/6).

%p gf:= exp(x*exp(x*exp(x)+x^2/2)+x^2/2*exp(x)+x^3/6):

%p a:= n-> n!* coeff(series(gf,x,n+1), x, n):

%p seq(a(n), n=0..30);

%t t[0, _] = 1; t[k_, x_] := t[k, x] = Exp[Sum[x^m/m!*t[k-m, x], {m, 1, k}]]; a[0, 0] = 1; a[_, 0] = 0; a[n_, k_] := SeriesCoefficient[t[k, x], {x, 0, n}]*n!; Table[a[n, 3], {n, 0, 30} ] (* _Jean-François Alcover_, Feb 04 2014, after A135302 and _Alois P. Heinz_ *)

%Y Column k=3 of A135302.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Mar 29 2012